Recursive computation of Hermite spherical spline interpolants

Let u   be a function defined on a spherical triangulation ΔΔ of the unit sphere S  . In this paper, we study a recursive method for the construction of a Hermite spline interpolant ukuk of class CkCk and degree 4k+14k+1 on S  , defined by some data scheme Dk(u)Dk(u). We show that when the data sets Dr(u)Dr(u) are nested, i.e., Dr-1(u)⊂Dr(u)Dr-1(u)⊂Dr(u), 1⩽r⩽k,1⩽r⩽k, the spline function ukuk can be decomposed as a sum of k+1k+1 simple elements. This decomposition leads to the construction of a new and interesting basis of a space of Hermite spherical splines. The theoretical results are illustrated by some numerical examples.